Abstract
We develop a framework to apply tropical and nonarchimedean analytic methods to multiplication maps for linear series on algebraic curves, studying degenerations of these multiplications maps when the special fiber is not of compact type. As an application, we give a new proof of the Gieseker–Petri theorem, including an explicit tropical criterion for a curve over a valued field to be Gieseker–Petri general.
| Original language | English |
|---|---|
| Pages (from-to) | 2043-2066 |
| Number of pages | 24 |
| Journal | Algebra and Number Theory |
| Volume | 8 |
| Issue number | 9 |
| DOIs | |
| State | Published - 2014 |
Bibliographical note
Publisher Copyright:©2014 Mathematical Sciences Publishers.
Funding
| Funders | Funder number |
|---|---|
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | 1135049, 1068689, 1149054 |
Keywords
- Chain of loops
- Gieseker–Petri theorem
- Multiplication maps
- Nonarchimedean geometry
- Poincaré–Lelong
- Tropical Brill–Noether theory
- Tropical independence
ASJC Scopus subject areas
- Algebra and Number Theory